Are there diquarks in the nucleon?

This work is devoted to the study of diquark correlations inside the nucleon. We analyze some matrix elements which encode information about the nonperturbative forces, in different color antitriplet diquark channels. We suggest a lattice calculation to check the quark-diquark picture and clarify the role of instanton-mediated interactions. We study in detail the physical properties of the $0^{+}$ diquark, using the random instanton liquid model. We find that instanton forces are sufficiently strong to form a diquark bound state, with a mass of $\sim 500\mathrm{MeV}$, which is compatible with earlier estimates. We also compute its electromagnetic form factor and find that the diquark is a broad object, with a size comparable with that of the proton.

Figure 1

Graphical representation of the integrand in Eq. (65).

Figure 2

Predictions for the ratio $R_1(r)={\rho }_{{\gamma }_3}(\mathbf{r})/{\rho }_{{\gamma }_5}(\mathbf{r})$ in the nonrelativistic quark model (NRQM), in the random instanton liquid model (RILM) and in the chiral soliton model (CSM). The CSM results include the projection onto the proton state.

Figure 3

Predictions for the ratio $R_2(\mathbf{r})={\rho }_{{\gamma }_4{\gamma }_5}(\mathbf{r})/{\rho }_{{\gamma }_5}(\mathbf{r})$, in the nonrelativistic quark model (NRQM), in the random instanton liquid model (RILM) and in the chiral soliton model (CSM).

Figure 4

Predictions for the ratio $R_3(\mathbf{r})={\rho }_{{\gamma }_4}(\mathbf{r})/{\rho }_{{\gamma }_5}(\mathbf{r})$ in the nonrelativistic quark model (NRQM), in the random instanton liquid model (RILM) and in the chiral soliton model (CSM). The CSM results include the projection onto the proton state. The nonrelativistic quark model curve is identically zero.

Figure 5

Logarithm of the diquark two-point function, $\ln G2(\tau )$ computed in the random instanton liquid model. The linear slope is a clean signature of the existence of a bound state.

Figure 6

The mass of the $u\mathrm{\text{−}}d$ diquark, computed in the random instanton liquid model, as a function of the $u$ and $d$ bare quark mass.

Figure 7

The diquark form factor (normalized to the total charge) evaluated in the random instanton liquid model (points) and compared with the dipole parametrization of the low-energy data on proton electric form factor: $F_{\mathrm{dip}}=1/(1+Q^2/0.71{)}^2$ (dashed line). The numerical simulation was performed in a $(4^3\times 6){\mathrm{fm}}^4$ box and the exchanged momentum is quantized accordingly.